Multiplying positives and negatives

We know that $5\times~2=10$, but what about $-5\times~-2$? Or $5\times~-2$?

To learn how to multiply positive and negative numbers, we will make a table and look for patterns. We will also begin with simple problems that we definitely know the answer to. Starting with answers we know, we will follow the pattern to discover the answers to unfamiliar questions.

We know that 5 • 3 = 15, 5 • 2 = 10, and 5 • 1 = 5 because they are the "times tables" we learned in earlier grades. Let's put these multiplication facts into a table and look for patterns.

(+5)(+3) = 15

In this table we can see that as the second number goes down by one, the product goes down by 5.

(+5)(+2) = 10

(+5)(+1) = 5

(+5)(0) = 0

(+5)(-1) = -5

(+5)(-2) = -10

(+5)(-3) = -15

Since multiplication is Commutative and (+5)(-3) equals -15, then this means (-3)(+5) is also equal to -15. This means we can make a new table with (-3) as the leading factor.

(-3)(+5) = -15

In this table we can see that as the second number goes down by one, the product goes up by 3.

(-3)(+4) = -12

(-3)(+3) = -9

(-3)(+2) = -6

(-3)(+1) = -3

(-3)(0) = 0

(-3)(-1) = +3

(-3)(-2) = +6

(-3)(-3) = +9

These two tables tell us all we need to know about multiplying positive and negative numbers.

When multiplying TWO positives and negatives, you just multiply the absolute values of the numbers. To determine the sign of the product, if both signs match, then the answer is positive and if the two signs are different, then the answer is negative.

How to multiply two numbers.

Multiply the absolute values of the two numbers.

If the two signs match, the product is positive.

If the two signs do not match, the product is negative.

Example 1:
Simplify (-4)(+7)

Begin by multiplying the absolute values of the two numbers, 4 • 7 = 28. Since -4 and +7 have different signs, the product is negative. The product of (-4)(+7) is -28.

Example 3:
Simplify (+3)(+9)

Both numbers are positive, so the product is positive. (+3)(+9) = +27.

Example 2:
Simplify (-6)(-9)

Since both numbers are negative, we automatically know the product will be positive. Multiplying the absolute values, we get 6 • 9 = 54. The product is +54.

Example 4:
Simplify (+8)(-7)

Begin by multiplying the absolute values of the two numbers, 8 • 7 = 56. Since +8 and -7 have different signs, the product is negative. The product of (+8)(-7) is -56.